ASTRONOMY FOR FIELD ARTILLERY
The FA surveyor can determine an accurate azimuth rapidly and easily by observation of the sun or stars. These astro observations provide true azimuths, which are converted to grid azimuths by applying grid convergence.
The FA surveyor uses practical astronomy to perform his mission. Practical astronomy is used to determine time, position, and azimuth. The FA surveyor observes celestial bodies only to determine azimuth. High-order survey organizations determine position by astro observation. The key to gaining a working knowledge of practical astronomy is learning its terms. The following paragraphs and the Glossary define the common astronomic terms.
a. The earth has the shape of a flattened sphere. The line connecting the flattened ends of the earth is the axis of the earth. The points at either end of this axis are the North and South Poles.
b. The earth has two important motions to the surveyor--rotation and revolution.
(1) Rotation. Rotation refers to the turning of the earth on its axis. The earth rotates from west to east, making one complete rotation in a period of about 24 hours. (See Figure 7-1.)
(2) Revolution. The earth revolves about the sun on a 600-million-mile orbit at a speed of about 18.5 miles per second. The average distance to the sun is 93 million miles. The earth's orbit is an ellipse, having the sun at one focus. The axis of the earth is tilted 23.5° from the perpendicular to the plane of its orbit around the sun. This tilting gives us our seasons. On the first day of spring and of fall, about the same amount of sunlight is received in both the Northern and Southern Hemispheres. During the winter in the Northern Hemisphere, no sunlight reaches the north arctic regions, which causes wintry weather to extend south to the lower latitudes. The reverse is true during the summer in the Northern Hemisphere. (See Figure 7-2.)
c. Since adapting a rectangular coordinate system to a sphere is impractical, a system using angular measurements was adopted.
(1) Latitude. Planes were passed through the earth, all parallel to each other and perpendicular to the rotating axis of the earth. The lines that these planes inscribe on the earth's surface are called parallels of latitude. The parallel of latitude halfway between the poles is called the equator. This parallel is given a value of 0° and is used as the basis for measuring latitude. Latitude is measured in units of degrees, minutes, and seconds north or south of the equator (34°48'12" N or 30°12'16" S) Up to 90°.
(2) Longitude. Other planes were passed through the earth so they intersect at both poles. The lines these planes inscribe on the surface of the sphere are called meridians of longitude. A baseline for measurement was established with the meridian that passed through Greenwich, England, and was given a value of 0°. Longitude is measured in units of degrees, minutes, and seconds east (E) and west (W) of the Greenwich meridian (for example, 90°24'18" W or 40°12'43" E) up to 180°.
a. In practical astronomy, the sun and stars are considered fixed onto a sphere of infinite radius. At the center of this sphere is the eye of an observer. The observer is assumed to be located at the center of the earth. This imaginary sphere of infinite radius is called the celestial sphere. The celestial sphere allows us to solve all problems of astro observations by using spherical trigonometry.
b. The celestial sphere appears to rotate about an axis. However, this apparent rotation is due to rotation of the earth about its axis from west to east in a counterclockwise movement and is opposite in direction to that in which the stars appear to move. In practical astronomy, the earth is regarded as stationary and the celestial sphere revolves about the earth from east to west.
a. Reference points, such as the poles, the equator, meridians of longitude, and parallels of latitude, are used to determine the location of points on the surface of the earth. Spherical coordinates are used to determine the location of points on the celestial sphere. There are two systems of spherical coordinates--the horizon system and the equator system. The artillery surveyor uses the equator system.
b. Since the earth is assumed to be the center of the celestial sphere, the North and South Poles of the earth can be extended to the sphere where they become the celestial North and South Poles. Likewise, the plane of the earth's equator, extended to the celestial sphere, becomes the celestial equator. (See Figure 7-3.)
c. The observer's position on earth is located by latitude and longitude. When the observer's plumb line is extended upward to the celestial sphere, the observer's zenith is established on the sphere. The arc distance between the zenith of the observer and the celestial equator is the same as the arc distance, in latitude, between his position on the surface of the earth and the earth's equator. The longitude of the observer is the arc on the equator between the Greenwich meridian (0° prime meridian) and the observer's meridian. On the celestial sphere, the longitude is the arc on the celestial equator between the planes of the Greenwich meridian and the meridian of the observer extended to intersect the celestial sphere. (It is also the angle at the pole between the planes of the two meridians.) When latitude and longitude are used in this manner and projected to the celestial sphere, the position of the observer's instrument is fixed at a point on the celestial sphere known as the zenith. (See Figure 7-4.)
d. The FA surveyor uses right ascension and declination to identify the location of a star on the celestial sphere. In the equator system of spherical coordinates, there must be points of origin. The points of zero reference in the equator system are the vernal equinox (VE) and the celestial equator.
(1) During each year, the sun traces a path, called the ecliptic, on the celestial sphere. This path is caused by the tilt of the minor axis of the earth with respect to the plane of its orbit. (See Figure 7-5.) This path of the sun moves from the Southern Hemisphere of the celestial sphere to the Northern Hemisphere and back. The point where the sun crosses the celestial equator in its movement from south to north along the ecliptic is known as the vernal equinox, the first day of spring. The vernal equinox is the first point of reference in the equator system of spherical coordinates. It also is used in the same manner that the prime meridian of Greenwich is used as a point of reference.
(2) The celestial equator, the plane of the earth equator extended to the celestial sphere, is the second point of reference. It divides the celestial globe into celestial Northern and Southern Hemispheres. The declination (see Glossary) of the celestial equator is 0° or 0 mils (e(2) below), just as the earth's equator is 0° or 0 mils latitude.
e. Since the stars appear to rotate about the earth, it is necessary to have a fixed point that can be readily identified and whose location in time relative to the Greenwich meridian can be computed for any given moment. (See the discussion of sidereal time in paragraph 7-7.) The fixed point is the vernal equinox, the point where the sun crosses the celestial equator from south to north on or about March 21, the first day of spring. Once the position of the vernal equinox is known, it is possible to identify the relative location of any prominent star by knowing how far it is from the vernal equinox and whether it is north or south of the celestial equator, the second fixed reference. (See Figure 7-6.)
(1) The spherical coordinate right ascension (RA) is the arc distance eastward along the celestial equator from the vernal equinox to the hour circle (see Glossary) of the star. It may be measured in degrees (°), minutes ('), and seconds (") of arc or in hours (h), minutes (m), and seconds (s) of time. The latter is the normal means of expression and can be from 0h to 24h east of the vernal equinox.
(2) Declination, the second spherical coordinate, is the star's angular distance north or south of the celestial equator measured on the hour circle of the body. North declination is plus (+), and south declination is minus (-). Declination can be from 0 mils to 1,600 mils north or south of the celestial equator. (See Figure 7-6.)
f. The observer's horizon is the plane tangent to the earth at the observer's position and perpendicular to his plumb line extended to the celestial sphere. The observer's horizon is used as a reference for determining the altitude of a celestial body. It is discussed in detail in paragraph 7-4.
a. In FA survey, the determination of astro azimuth is based on the solution of a spherical triangle, a triangle located on the celestial sphere. The celestial spherical triangle has the vertices of the pole (P), the observer's zenith (Z), and the sun or star (S). This triangle is known as the astronomic, or PZS, triangle (See Figure 7-7.)
b. The sides of the PZS triangle are segments of great circles passing through any two of the vertices. Hence, the sides are arcs and are measured with angular values. The angular value of each side is determined by the angle that the side subtends on the earth. (See Figure 7-8.) The three sides of the PZS triangle are the polar distance, the coaltitude, and the colatitude.
(1) Polar distance. The side of the PZS triangle from the celestial North Pole to the celestial body is called the polar distance (See Figure 7-9.) The value of the polar distance side is determined from the declination of the celestial body observed. Declination may be defined as the angular distance from a celestial body to the celestial equator. When the celestial body lies north of the celestial equator, the declination is plus. When the body lies south of the celestial equator, the declination is minus. The polar distance side is determined by algebraically subtracting the declination of the celestial body from 1,600 mils.
(2) Coaltitude. The side of the PZS triangle from the celestial body to the zenith is called coaltitude. (See Figure 7-10.) The coaltitude is the arc distance from a celestial body to the observer's zenith (zenith distance). This arc distance value is determined by subtracting the observed altitude of the celestial body (the sun corrected for refraction and parallax and stars corrected only for refraction) from 1,600 mils.
(3) Colatitude. The colatitude is the side of the triangle extending from the celestial North Pole to the zenith. (See Figure 7-11.) It is determined by subtracting the latitude of the observer from 90° (1,600 mils) when the observer is in the Northern Hemisphere. If the observer is in the Southern Hemisphere (that is, from 0° to 90° south), the colatitude is 90° (1,600 mils) plus the amount of south latitude.
c. The three angles formed by the three sides of the PZS triangle are the parallactic angle; the zenith, or azimuth angle; and the time angle (angle t). (See Figure 7-12.)
(1) The interior angle at the celestial body formed by the intersection of the polar distance side and the coaltitude side is called the parallactic angle. It is used in determining azimuth by the arty astro method but cancels out in the computations.
(2) The interior angle at the zenith formed by the intersection of the coaltitude side and the colatitude side is referred to as the zenith, or azimuth angle. This angle is the product of the computations and is used to determine true azimuth from the observer to the celestial body. When the celestial body is in the east, the azimuth angle is equal to the true azimuth. When the celestial body is in the west, true azimuth equals 6,400 mils minus the azimuth angle.
(3) The interior angle of the PZS triangle formed at the pole by the intersection of the polar distance side and the colatitude side is called the time angle, or angle t.
d. If the artillery surveyor knows any three elements of the PZS triangle, the other elements can be determined by spherical trigonometry. The element the artillery surveyor always solves for is the angle from the pole to the celestial body measured at the zenith (azimuth angle). This angle is used in establishing a true azimuth on the ground. Once the artillery surveyor becomes familiar with the procedures for measuring and recording the field data necessary to solve the azimuth angle of this triangle, he finds that the solution is no more difficult than solving a plane triangle established on the earth's surface. Therefore, the artillery surveyor must understand how to obtain the essential astro field data. Obtaining these data requires a limited knowledge of star identification and how to use the Army ephemeris and DA forms designed to simplify the solution of the various formulas.
e. Since each PZS triangle is constantly changing because of the apparent rotation of the celestial sphere, the solution for the unknown must be related to specific time. Therefore, accurate time becomes a highly significant consideration in astro survey operations.
a. All astro observations are made on celestial objects that are in constant apparent motion with respect to the observer. To make use of these observations and to solve the PZS triangle, the surveyor must have one other factor. He must know the precise time of the observation so that he can fix the position of the terrestrial or horizon system of coordinates in relation to the celestial coordinate system. In the field of practical astronomy, two categories of time are used. These are sun (or solar) time and star (or sidereal) time.
b. Both classes of time are based on one rotation of the earth with respect to a standard reference line. Because of the motion of the earth in the plane of its orbit around the sun once each year, this reference line to the sun is continually changing (Figure 7-13) and the length of the solar day is not the true time of one rotation of the earth on its axis. For the purpose of practical astronomy, the true rotation of the earth is based on one rotation of the earth on its polar axis with respect to the vernal equinox and is known as the sidereal day. Therefore, the lengths of the sidereal day and the solar day differ. The solar day is longer by 3 minutes and 56 seconds. The FA surveyor does not have to understand this differential in the lengths of the solar and sidereal days to compute azimuth data derived from astro observations. However, he will be more effective if he does, because he can then more readily adjust to the continually changing view of the stars overhead. The explanation of the differential, while it is simple, requires a departure from the concepts of a motionless earth and a revolving celestial sphere and sun. Instead, the concept of a motionless celestial sphere with the sun as the center and the earth in motion is used as the basis for the explanation.
c. Since the earth completes one orbit of the sun in 365 and a fraction days, it may be stated that because of the orbital motion of the earth, the sun has an apparent eastward motion among the stars of about 1° per day. This motion of the sun makes the intervals between the sun transits of the observer's meridian about 4 minutes greater than the interval between transits of the VE of the observer's meridian. Therefore, the solar day is nearly 4 minutes longer than the sidereal day. (See Figure 7-13.)
d. Because for purpose of practical astronomy one apparent rotation of the celestial sphere is completed in a sidereal day, a star rises at nearly the same sidereal time throughout the year. On solar time, it rises about 4 minutes earlier from night to night, or 2 hours earlier from month to month. Thus, at the same hour, day by day, the stars move slowly westward across the sky as the year lengthens.
a. The solar day, or the time corresponding to one rotation of the earth with respect to the direction of the sun, is the most natural unit of time for ordinary purposes. If time was regulated by stars, sidereal noon would occur at night during half the year. For obvious reasons, this would not be a satisfactory condition. Also, to begin the solar day when the sun crosses the observer's meridian would result in confusion. So to keep an orderly scheme of things, we start the solar day when the sun crosses the lower meridian of the observer. The instant of time when the sun is on the lower branch of the observer's meridian is defined as solar midnight. When the sun crosses the upper branch of the observer's meridian, it is solar noon at the observer's location. This arrangement would be satisfactory except that the solar day varies in length. This is because the rate at which the sun moves along the ecliptic is inconsistent and the orbital path of the earth around the sun is elliptical. This deviation in the length of the solar day varies from season to season, which makes using this variable day as a base for accurate time almost impossible. Modern conditions demand accurate measurement of time. Therefore, the mean solar day, an invariable unit of time, was devised. It is based on a fictitious, or mean, sun which is imagined to move at a uniform rate in its apparent path about the earth. It makes one apparent revolution around the earth in 1 year, as does the actual sun. The average apparent solar day was used as a basis for the mean solar day. The time indicated by the position of the mean sun is called mean solar time. The time indicated by the position of the actual sun is called apparent solar time. The difference between the two times is called the equation of time, and it varies from minus 14m (mean sun fast) to plus 16m (mean sun slow), depending on the season of the year. (See Figure 7-14.)
b. The year defined by the fictitious, or mean, sun (tropical year) is divided into 365.2422 mean solar days. Time based on these days of constant length is called mean solar time, or civil time. Since the mean sun appears to revolve around the earth every 24 hours of mean time, the apparent rate of movement of the mean sun is 15° of arc, or longitude, per hour (360 ÷ 24 = 15).
c. In the geographic coordinate system (latitude and longitude), the primary and secondary planes of reference are the earth equator and the meridian that passes through Greenwich, England (the prime meridian), respectively. When the Greenwich meridian is used as a basis of reference, time at a point 15° west of the Greenwich meridian is 1 hour earlier than the time at the Greenwich meridian, because the sun passes the Greenwich meridian 1 hour before it crosses the meridian lying 15° to the west. The opposite is true of the meridian lying 15° to the east, where time is 1 hour later, since the sun crosses this meridian 1 hour before it arrives at the Greenwich meridian. Therefore, the difference in local time between two places equals the difference in longitude between the places. (See Figure 7-15.) To further expedite time conversions, two basic reference meridians have been selected as common references. These are the Greenwich meridian and the 180th meridian. The main classes of time used by the artillery surveyor in his use of practical astronomy are, in some manner, related to these basic reference meridians. Subsequent definitions and explanations make use of these basic reference meridians.
d. Since the mean solar day has been divided into 24 equal units of time, there are 24 time zones, each 15° wide, around the earth. With the Greenwich meridian, 0° longitude, used as the central meridian of a time zone and the zero reference for the computation of time zones, each 15° zone extends 7.5° east and west of the zone central meridian. Therefore, the central meridian of each time zone, east or west of the Greenwich meridian, is a multiple of 15°. For example, the time zone of the 90° meridian extends from 82°30' to 97°30'. (See Figure 7-16.) Each 15° meridian, or multiple of, east or west of the Greenwich meridian is called a standard time meridian. Four of these meridians (75°, 90°, 105°, and 120°) cross the United States. (See Figure 7-17.)
e. Standard time zone boundaries are often irregular, especially over land areas. Standard time zone boundaries follow the 7.5° rule to each side of the zone central meridian, approximately, having been shifted wherever necessary to coincide with geographical or political boundaries. Standard time, a refinement of mean solar time, is further identified by names and/or letter designations. For example, the central standard time (CST) zone, time based on the 90° meridian, is also the S standard time zone. (See Figure 7-18.) The artillery surveyor uses the term local mean time (LMT) in referring to standard time. It refers to the standard time in the referenced locale. Local mean time in artillery survey operations means the standard time for the area in which the observer is located. Therefore, LMT is clock time in the area unless the area is using nonstandard time such as daylight saving time.
f. To preclude the problem of compiling time data for each of 24 standard time zones of the world, it was decided to compute time data pertaining to mean solar time for only one of the standard time zones. Standard time zone Z (Figure 7-18), which uses the Greenwich meridian as its basic time meridian, was the zone chosen. Greenwich standard time, also known as Greenwich mean time (GMT) or Universal time, is defined as the length of time since the mean sun last crossed the 180th meridian (lower branch of the Greenwich Meridian) or solar midnight. This time can be expressed as the reading of the standard 24-hour clock at the Greenwich Observatory, Greenwich, England, at the moment an observation is made on a celestial body; hence, it is the same time throughout the world. Therefore, since the observer's watch is usually set on the standard time observed in his area, that time (LMT) must be converted to GMT. The data published in FM 6-300 are tabulated with respect to the Greenwich meridian and 0h Greenwich time.
*Note. When local time for an area of operation is unknown or suspect, use universal time (Zulu time) and a time zone correction of 0 hours. When the prompt is for time zone letter instead of time zone correction, use "Z." Universal time can be obtained from the survey time cube, GPS, or the SPCE.
g. To convert local mean time to Greenwich mean time when the observer is located in west longitude, divide the value of the central meridian of the time zone in degrees of longitude by 15°. This equals the time zone correction in hours. Add to the LMT the difference in time between the standard time zone of the observer's position and GMT to determine the GMT of observation. (See Figure 7-19.) If the result is greater than 24 hours, drop the amount over 24 hours and add 1 day to obtain the Greenwich time and date. When the observer is located in east longitude, subtract the time difference from the LMT to determine the Greenwich mean time of observation. If subtraction cannot be performed, add 24 hours to the LMT and drop 1 day to determine the Greenwich date of observation.
h. When the artillery surveyor makes observations on the sun, obviously he observes the apparent sun instead of the mean sun on which his time is based. Consequently, the observer must convert the Greenwich apparent time (GAT) of observation to the GMT. The date of observation is used as an argument to enter Table 2 of FM 6-300, and the value of the equation of time for zero hours GMT (0h) is extracted along with the daily change. The resultant equation of time value for the date and time of observation is then added algebraically to the GMT of observation.
i. Determining the local hour angle (LHA) of the sun, a value necessary for some astro formulas, requires several steps in addition to those in the example above. When the position of the apparent sun at the time of observation has been determined and related to the Greenwich meridian, the time is referred to as Greenwich apparent time. By simply adding 12 hours to, or subtracting it from, the GAT (the result cannot exceed 24 hours), the surveyor determines the value of the Greenwich hour angle (GHA). The Greenwich hour angle is the amount of time that has elapsed since the sun last crossed the Greenwich upper meridian. The next step is to convert both the observer's longitude, extracted from a trig list or scaled from a map, and the Greenwich hour angle to mils of arc. The arc distance (in mils) measured from the Greenwich meridian to the observer's meridian is added to the GHA in mils if the observer is located in east longitude. It is subtracted from the GHA in mils if he is located in west longitude. The result is the local hour angle of the apparent sun expressed in mils of arc. The final step is to determine angle t, the angle at the polar vertex of the PZS triangle. Angle t is determined as discussed below.
(1) If the local hour angle is greater than 3,200 mils, angle t equals 6,400 mils minus LHA.
(2) If the local hour angle is less than 3,200 mils, angle t equals LHA.
a. The sidereal day is defined by the time interval between successive passages of the vernal equinox over the upper meridian of a given location. The sidereal year is the interval of time required for the earth to orbit the sun and return to its same position in relation to the stars. Since the sidereal day is 3 minutes 56 seconds shorter than the solar day, this differential in time results in the sidereal year being 1 day longer than the solar (tropical) year, or a total of 366.2422 sidereal days. Since the vernal equinox is used as a reference point to mark the sidereal day, the sidereal time for any point at any instant is the hours, minutes, and seconds that have elapsed since the vernal equinox last passed the meridian of that point.
b. In general, it can be stated that observations on the sun involve apparent solar time, whereas observations on the stars are based on sidereal time. The computations using either apparent solar time or sidereal time are similar in that they do nothing more than fix the locations of both the celestial body and the observer in relation to the Greenwich meridian. Once a precise relationship has been established, it is a simple matter to complete the determination of azimuth to the celestial body.
ASTRONOMIC OBSERVATION TECHNIQUES
The technique used to observe a celestial body depends on the azimuth determination method used (altitude, arty astro observation, or Polaris tabular) and the type of celestial body being observed. Using the proper techniques will ensure more accurate results.
Astro observations can be used for, but are not limited to, the following survey operations:
- Determining or checking a starting azimuth for a conventional survey.
- Determining or checking the closing azimuth of a conventional survey.
- Checking the azimuth of any line in a survey.
- Providing orienting azimuths for cannons and associated fire control equipment.
- Determining azimuths for the declination of aiming circles.
- Providing orienting azimuths for radars and OPs.
The artillery surveyor uses three basic methods to determine azimuth by astro observation--the altitude method, arty astro observation, and Polaris tabular method. All three methods require a horizontal angle from an azimuth mark to the observed body to materialize the astro azimuth on the ground.
a. In the altitude method (Figure 7-20), the PZS triangle is solved by using the known data and the three sides of the triangle. In addition to the angle from a ground point to the celestial body, three elements must be determined. These elements are as follows:
- Latitude for determining the side colatitude.
- Declination of the body for determining the side polar distance.
- Attitude for determining the side coaltitude.
b. In the arty astro method (Figure 7-21), the azimuth angle is determined from two sides and the included angle. The sides are the polar distance and colatitude and must be determined as described in paragraph 7-4b. The angle at P (Figure 7-21) is angle t. The value of the local hour angle is computed by using the time of the observation and is then used to compute angle t.
c. In the Polaris tabular method, the azimuth to Polaris is tabulated in the Army ephemeris for every 3 minutes of local sidereal time (LST). The listed azimuth is corrected for the observer's latitude and the date of observation. This method avoids lengthy PZS triangle solutions, but it can be used only in the Northern Hemisphere.
a. Each of the three methods of determining azimuth by astro observation requires the measurement of the horizontal angle from the azimuth mark to the celestial body. The altitude method also requires measurement of the vertical angle. (See Figure 7-22.) Except for the method of pointing on the celestial body, horizontal and vertical angles are measured in the same way that angles are measured in traverse. A set of astro observations consists of horizontal angles measured one position and vertical angles measured by one direct and one reverse pointing.
b. In all astro observations, the instrument must be perfectly level with reference to the most sensitive bubble the instrument has. An appreciable error, which cannot be eliminated by direct and reverse pointing, is introduced into the measurement of a horizontal angle between two objects of considerable difference in elevation if the vertical axis of the instrument is not vertical.
Data required for computing astro azimuth differ slightly according to the method used.
a. Altitude and Polaris tabular methods require the following data:
- Latitude of the observer (correct to the nearest second).
- Longitude of the observer (correct to the nearest second).
- Horizontal angle from the desired azimuth mark to the celestial body.
- Approximate azimuth to the desired azimuth mark. A magnetic or map-spotted azimuth will suffice.
- Date of observation.
b. In addition to the data in a above, the altitude method requires the following data:
- Temperature (correct to nearest 5°).
- Vertical angle to the celestial body.
- Time of observation.
--Sun (accurate to the nearest 5 minutes).
--Star (accurate to the nearest day).
c. In addition to the data in a above, the Polaris tabular method requires time accurate to the nearest minute.
d. The arty astro method of observation requires the following data:
- UTM coordinates (easting and northing) map-spotted to within 150 meters.
- Horizontal reading from the desired azimuth mark to the celestial body.
- Approximate azimuth to the desired azimuth mark. A magnetic or map-spotted azimuth will suffice.
- Date of observation (manual input or BUCS time module).
- Time of observation (manual input or BUCS time module).
--Sun (accurate to 1 second).
--Star (accurate to 1 second).
--Polaris (accurate to 10 seconds).
(1) For the sun to be suitable for use with the altitude method, it should be within 530 mils of the observer's prime vertical. To determine if it is, algebraically subtract the declination of the sun on the local date from the latitude of the observer's station. The remainder is the angle from the prime vertical to the sun at noon. When he is observing the stars, the observer will have little difficulty in selecting stars that fall within the 530-mil requirement. The celestial bodies (sun or stars) should be observed between 175 mils and 800 mils in altitude. The sun should not be observed within 2 hours local apparent time of the observer's meridian, because there is no valid solution when the coaltitude side of the triangle is less than 30° (2 hours).
Note. The restriction has been placed on vertical angles over 800 mils because of the error introduced into the horizontal angle measurement when the instrument has not been leveled perfectly. The error in the horizontal angle is equal to the tangent of the altitude of the celestial body multiplied by the error in leveling the plate of the instrument. In the case of the T16 or T2 theodolite, one division of error in the plate level bubble is equal to an error of about 0.1 mil if the altitude angle is 800 mils. If the altitude angle is 1,000 mils, the error in the horizontal angle will be about 0.2 mil. For this reason, special precautions must be taken in leveling the instrument when a vertical angle between 800 and 1,100 mils is required.
(2) When the arty astro method is used, the sun should not be observed within 1 hour local apparent time of the observer's meridian. This is because there is no valid solution when angle t is less than 15° (1 hour).
(3) The selection of Polaris in the Northern Hemisphere or Alpha Acrux (Southern Cross Star) in the Southern Hemisphere should be automatic. The altitude of Polaris roughly coincides with the north latitude of the observer. Circumpolar stars are preferred to east-west stars.
(4) The arty astro method is the only acceptable method used with circumpolar stars other than Polaris.
(5) For best results, stars should be below 800 mils in altitude.
a. Temperature and a time correction should be obtained at the time of observation and checked after the final observation. The temperature may be obtained from meteorological (met) stations, powder thermometers, or any thermometer available. Time may be obtained from radio time signals (paragraph 7-32) or from the div arty SPCE. Message center and commercial radio times are generally accurate enough for altitude observations.
b. The BUCS contains an accurate quartz-crystal clock. Properly set, it will keep accurate time, within tenths of a second, until battery life expires or the memory is cleared. Any good watch with a sweep second hand is adequate for timekeeping, if a correction is carried. For astro observation, a good watch is one that gains or loses a constant amount of time over a given period. The timekeeper should not try to set his watch to the exact time, but he must ensure that the second hand is in the vicinity of 12 when the minute hand is on a minute mark. (This will preclude a 30-second error.) The timekeeper will determine the amount his watch is in error and note the correction, with the proper sign, in the remarks section of the recorded field notes.
a. When the sun is being observed, special pointing techniques are required to resolve its center because of the size and brilliance of the sun. Since the angular diameter of the sun is about 9.5 mils of arc, an accurate pointing cannot be made on the center of its disk without the use of special aids and/or techniques.
b. One of the special pointing aids is the solar circle etched on the reticle of the observing instrument. Most theodolites have the solar circle etched on the reticle. (See Figure 3-4.) No special pointing technique is required with these instruments, but the sun must be centered in the circle. The sun will not always fit exactly into the circle. However, the amount of overlap, or spacing, will not affect the final result.
c. Pointings on stars are made so the intersection of the vertical and horizontal cross hairs bisects the star.Chapter 3. With the instrument telescope in the direct position, he points the telescope at the azimuth mark. After the initial circle setting has been recorded in the recorder's book, the instrument operator and recorder perform the steps discussed below.
The sun must never be viewed through the telescope without a sun filter. The filter should be inspected before use to ensure that the coated surface is free from scratches or other defects. Serious eye damage will result if proper precautions are not taken.
Note. If the sun filter has been damaged or lost, a solar observation may be completed by use of the card method. The image of the sun is projected onto a card held 3 to 6 inches behind the eyepiece and the telescope is focused so that the cross hairs are clearly defined.
Note. Vertical angles are not measured for the arty astro or Polaris tabular methods.
*(4) The instrument operator then plunges the telescope to the reverse position, again sights on the sun, and announces TRACKING. The steps in (2) and (3) above are then repeated. The observer then sights on the azimuth mark and reads the horizontal circle reading. The recorder records the reading and determines the mean data. This completes one set of observations.
*Note. When using the arty astro method of observation, the instrument operator takes three direct readings to the celestial body, then plunges the telescope, and sights back on the azimuth mark. A second set should be taken with three readings in the reverse position as a check on the instrument and operator. As a rejection criteria, the closing readings on the azimuth mark should agree with the initial circle setting by the known spread of the instrument. In addition, the mean of the two sets of readings should agree with both sets within prescribed accuracies.
b. Three sets of observations must be made normally by the procedures in a above. However, a well-trained observer may use a modified form of these procedures. A modified form would be to take three direct observations and then three reverse observations before closing the angles on the azimuth mark. Care must be taken in recording the observations.
c. Pointings on the stars are made in the same manner as pointings on the sun except that at the instant TIP is announced the cross hairs should bisect the star.
Note. When the observer is observing the stars it is advantageous for him to have the telescope blacked out until the star is identified. When the star has been identified, the telescope light rheostat is turned up so that as many stars as possible, other than the desired one, will be obliterated by the light in the telescope.
a. The format for recording field data and determining the mean angles is generally the same as that for other angle measurements except for the large spread between the direct and reverse readings and that the times of observation are recorded. The mean time of observation is determined from the times recorded for the direct and reverse pointing. The same format is used for observations with the T16 and T2 theodolites. Sun observations are recorded in the same manner as star observations, Figures 4-12, 4-13, 4-15, and 4-20 show how data are recorded in a field notebook for astro observations.
b. Extreme care must be taken in meaning time. Time is recorded in three units--hours, minutes, and seconds. If using a watch to record time, record seconds first, followed by minutes and hours. Time should be meaned by using the method described in the following example.
THE ARMY EPHEMERIS
The Army ephemeris (FM 6-300) is a condensation of data from the American Ephemeris and Nautical Almanac. Units must request FM 6-300 from the AG Publications Center or be on pinpoint distribution. It is issued to artillery units equipped to perform astro observations. Data in the tables of FM 6-300 are required in computing direction from astro observations. All data extracted from the ephemeris tables will be expressed to the accuracy of the ephemeris. The use of the ephemeris tables is explained in this section. Sample problems are based on data in the ephemeris for 1993 through 1997. Only the tables used by the artillery surveyor are explained herein.
7-16. TABLE 1b, ASTRONOMIC REFRACTION CORRECTED FOR TEMPERATURE (MILS)
a. Table 1b of FM 6-300 is used to determine the value of the refraction correction. This correction is applied to vertical angles measured to either the sun or the stars. Refraction is the apparent displacement of a celestial body caused by the bending of light rays passing through layers of air of varying density. The celestial body appears higher than it really is. Therefore, the sign of the correction is always minus.
b. To determine the value of the refraction correction, use as arguments the mean vertical angle (observed altitude) and the mean temperature at the time of observation. Arguments for temperature increase in units of 10° from -30°F to + 130°F. Arguments for observed altitude increase in units of 10 mils from 0 mils through 1,200 mils. When the observed altitude and temperature are not tabulated in the table, enter the table with the values nearest those observed. For example, to determine the refraction correction for a mean vertical angle of 697 mils and a temperature of +93°F at the time of observation, examine the table. The nearest tabulated altitude is 700 mils, and the nearest temperature is +90°F. Enter the table at 700 mils, and move right to the column for 90°F. Extract the refraction correction of 0.32 mil. Should the mean vertical angle fall exactly halfway between two tabulated altitudes, use the higher tabulated altitude. Should the temperature fall exactly halfway between two tabulated temperatures, use the lower tabulated temperature. For example, to determine the refraction correction for a mean vertical angle of 745 mils, which is halfway between two tabulated altitudes (740 mils and 750 mils), select the higher value (750 mils). For a temperature of 95°, halfway between two tabulated temperatures (+90° and +100°), select the lower (90°). Extract the refraction correction of 0.29mil.
Table 2 is divided into three major parts--apparent declination (shown in both degrees and mils), equation of time, and sidereal time. Each of the major parts is discussed separately. The first column is common to all three parts of Table 2 and contains the Greenwich dates and days of the week for the entire year.
a. Apparent Declination. The declination of a celestial body is the angular distance from the celestial equator measured along the hour circle of the body. Declination, which is positive when the body is north of the celestial equator and negative when it is south of the celestial equator, corresponds to latitude on earth. The declination of the sun is tabulated for 0 hours GMT for each day of the year, and the daily change in declination is shown in the DAILY CHANGE (SEC) column. The algebraic signs of the declination and the daily change are critical and must be included. When the BUCS is used, the value of apparent declination in degrees, minutes, and seconds is determined to the nearest second.
b. Sidereal Time. The local sidereal time is the number of hours, minutes, and seconds that have elapsed since the vernal equinox last crossed the observer's meridian. The Greenwich sidereal time is the hours, minutes, and seconds that have elapsed since the vernal equinox last crossed the Greenwich meridian. Sidereal time is used when Polaris tabular observations have been made and it is necessary to convert mean time to sidereal time. The sidereal time to the nearest second is extracted from Table 2.
Table 9 is an alphabetical list of 73 stars, the constellation in which each star is found, the number of each star, and the magnitude of each star. This table is used primarily to provide the star numbers to determine data on the stars from Table 10. The constellation and magnitude aid in identifying the star. For example, find the star Enif in the list. The table shows that Enif is in the constellation Pegasus, is star number 70, and has a magnitude of 2.5.
Tables 10a and 10b contain the declination for all the stars listed in Table 9 except Polaris. In Table 10a, declination is in degrees. Table 10b lists declination in mils. Right ascension and declination are given for the first day of each month. Values for other dates are interpolated as discussed below.
a. Determine the difference for both right ascension and declination (in seconds) from the first of the month to the first of the following month. Use the proper algebraic sign.
b. Divide the number of days past the first of the month by 30 days (standard month). Multiply the result by the difference determined in a above to obtain the changes in right ascension and declination from the first of the month.
c. Apply the change determined in b above to the declination at the first day of the month to determine the declination for the given day.
Table 11 contains the declination (in degrees and mils) and the right ascension of Polaris. The values listed are for 0 hours GMT on the 0, 10th, 20th, and 30th days of each month (10-day) intervals). To determine the declination or the right ascension of Polaris for a given day, interpolate between the given values. Data for the 31st day of the month are shown as the 0 day of the following month.
The artillery surveyor uses Table 12 only to determine azimuth by the Polaris tabular method. Correct time should be known to the nearest 1 minute.
a. Extraction of b0. The argument used for extracting b0 is local sidereal time and current year. The hours of local sidereal time are listed in column headings across the page, and the minutes of LST are listed vertically at the left of the hour columns.
b. Extraction of b1. The arguments used to extract b1 are the same hour column used to find and the observer's latitude.
c. Extraction of b2. Find the value of b2 by entering the bottom section of the table with the hour (same column as for b0 and b1) and Greenwich date. From the 1st to the 15th day of the month, use the Greenwich month of observation. From the 16th to the last day of the month, use the month after the Greenwich month of observation.
Table 13 is a nomograph for determining the grid azimuth correction in a simultaneous observation. Use of this table is explained in Section IX of this chapter.
STAR SELECTION AND IDENTIFICATION
There are important advantages to using stars rather than the sun as sources of astro azimuth. Since they appear as pinpoints of light in instrument telescopes, stars are easier to track than the sun. At least one of the 73 stars tabulated in the Army ephemeris can usually be found in a satisfactory position for observation regardless of the time of night or the observer's latitude. The North Star (Polaris) should always be used when the geographical location and tactical situation permit. Polaris is the most desirable source of astro azimuth because it is easily identified and because its slow apparent motion makes it easy to track. The Polaris tabular method yields reliable azimuths in considerably less time than any other method. In the low northern latitudes and the Southern Hemisphere, however, east-west (noncircumpolar) stars must be used for night astro azimuth determination. Local weather conditions obscuring Polaris may also make observation of east-west stars necessary. Since so many stars are available for observation, the artillery surveyor must be able to select and identify those most suitable for observation. The star finder and identifier is used to identify them.
The star finder and identifier (Figure 7-23) is a device used to determine the approximate (±2°) azimuth and altitude of a given star. This device is issued as a component of the survey set, artillery fire control, fourth-order. The star finder and identifier consists of a base, 10 templates, and a carrying case. The base is reversible with stars of the Northern Hemisphere on one side and stars of the Southern Hemisphere on the other. There is one template for each 10° of latitude from 5° to 85° (5°, 15°, 25°, 35°, and so forth). (The tenth template, designed for plotting the sun and planets, is not used in artillery survey). Each template is reversible with one side for north latitude and the other side for south latitude. The template constructed for the latitude nearest the latitude of the observer should be used. The base of the star finder in Figure 7-23 shows the stars visible in the Northern Hemisphere. The center of the device represents the celestial North Pole. The edge of the base is a circle graduated in degrees and half degrees, representing the local hour angle of the vernal equinox or the local sidereal time. On each template is a series of concentric ellipses. Around the outer edge of these ellipses are two sets of numbers from 0° to 360°. The inner set of numbers starts at the top of the template for north latitude and increases in a clockwise direction. The outer set of numbers starts at the bottom of the template for south latitude and increases in a clockwise direction around the ellipses. In the Northern Hemisphere, the inner figures are used; in the Southern Hemisphere, the outer figures are used. The inner set of figures represents the azimuth from the celestial North Pole to the line that the figures identify. The outer set of figures represents the same thing except that the azimuth is from the celestial South Pole to the line. The series of concentric ellipses represents altitudes above the horizon. The template has the horizon on its circumference, the zenith as its center, and a measure of azimuth around the edge. The 0° to 180° line represents the observer's meridian. Before the star finder can be oriented, the value of the local sidereal time must be determined. The pointer of the template is then placed over the appropriate value on the base of the star finder. Local sidereal time can be determined by using DA Form 7284-R (Computation of Star Identification (BUCS)) or by using the Haught method for orienting the star finder and identifier.
This is a simple method of computing the LST for orienting the star finder and identifier. The results are accurate to within 1° and can be used for any time or location. The final result is the LST for 1900 on the date of observation. Use the time-arc relationship to adjust for different observation times. One hour is equal to 15° of shift on the star finder and identifier, and 4 minutes is equal to 1° of shift. To compute the LST by using the Haught method, follow the procedures discussed below.
a. Count the number of months this year preceding the observation month. Multiply that number by 30.
b. Add the observation date.
c. Add a constant of 24.
d. Determine the difference between the observer's longitude and the longitude of the central meridian of the observer's time zone. Add the difference if the observer is east; subtract if west.
e. If using daylight saving time (DST), subtract 15. DST in the US is from the first Sunday in April to the last Sunday in October. The result is the LST (orienting angle) to set on the star identifier for 1900.
f. Determine the difference between 1900 and the time of observation. (Each hour is equal to 15°, and each 4 minutes is equal to 10.) Add if the observation time is after 1900, and subtract if the observation time is before 1900.
a. The apparent motion of a celestial body has two components--a horizontal motion, representing change in azimuth, and a vertical motion, representing change in altitude. An error in measuring the altitude of a celestial body will result in a final azimuth error related to the ratio between the two components of the apparent motion of the body. (See Figure 7-24.) When a star is moving at a small angle to the horizon, an error in measuring the altitude will result in a greater error in final azimuth than it would if the star were moving at a large angle to the horizon. (See Figure 7-25.) This relationship is called the star rate, which is the ratio of resulting azimuth error to error in vertical measurement. A star that changes in altitude but not in azimuth will have a star rate of 0, since an error in altitude measurement will result in no error in azimuth. A star that changes so rapidly in azimuth and so slowly in altitude that a 1-mil error in attitude measurement will result in a 3-mil azimuth error has a star rate of 3.
b. For altitude method observations, select the stars with the lowest star rates, since both azimuth and altitude are measured. Low star rates are not essential for arty astro observations, because altitude is not measured. However, stars with low star rates will be moving more slowly in azimuth and will be easier to track than those with high star rates. Although Polaris has a high star rate in its culminations, its apparent motion is so slow that it can be observed successfully at any time. Avoid observing stars below 175 mils in altitude because of possible errors caused by refraction.
a. A map depicts the prominent points on the earth, and the star chart depicts the prominent points in the sky. (See Figure 7-26.) On the earth latitude and longitude are used to fix the location of points; declination and right ascension are generally used to fix the stars at definite coordinates. Consequently, on a star chart the north-south location of a star is fixed by declination, and the east-west location is fixed by right ascension.
b. The two projections by which star charts are plotted are cylindrical (similar to the mercator projection for world maps) and plane (similar to polar projection for world areas). The cylindrical projection presents great distortion about the poles of the celestial sphere but offers a fairly accurate picture in declination to ±65°. It should be remembered that in such a projection the vertical lines plotted to be parallel actually converge at the poles and are perpendicular to the equator. The plane projection presents a truer picture of the sky, especially if it is used with a mark that blocks out all the sky except that within the horizon for a given area.
c. The brightness of stars is measured in magnitude. Thus, the brightest stars are of the first magnitude, the next in brightness are of the second magnitude, and so forth. Stars in constellations, some of which have individual names (for example, Polaris), are usually named in the constellation in order of their brightness through the use of the Greek alphabet. Thus, in the constellation Orion, from the brightest to the least bright, the stars are named (Betelgeuse [also Betelgeux]), (Rigel), (Bellatrix), and so forth. The magnitude of each star is shown on star charts.
(1) Determine the LST of observation from Figure 7-27.
(a) Enter the table with the closest date of observation.
(b) From the date, move to the right and stop in the column of the closest hour of observation.
(c) Extract the LST from the hour column.
(2) Locate the celestial equator.
(a) Subtract the observer's latitude from 90°. The result is the distance above the horizon to the celestial equator.
(b) Face south, and determine the position of the celestial equator. Remember, at arms length, a finger width is 2°, 1 hand width is 10°, and 1 hand span is 20°.
(3) Hold the world star chart with the word North on top. Locate the graduation at the top the chart that represents the LST. Face south, and align the LST graduation just below the celestial equator along the observer's meridian. The world star chart is now oriented with the stars in the sky.
e. The following method can be used to orient the world star chart in the Southern Hemisphere.
(2) Locate the celestial equator. This is done the same as in the Northern Hemisphere except the observer must face north and count up from the horizon to locate the celestial equator.
(3) Hold the world star chart with the word South at the top. Locate the graduation at the top of the chart that represents the LST. Face north, and align the LST graduation just below the celestial equator along the observer's meridian.
f. To aid the observer, highlight the 30° N and 30° S lines on the star chart. Also highlight the 0° line, which is the celestial equator. The strip of sky as outlined by the 30° N and 30° S lines will contain the brightest stars (seen at any one time). Keep in mind that the strip of sky being looked at is about 6 hours either side of the LST.
The easiest way to identify stars and fix their locations in relation to each other is to learn something about constellations. Since stars are fixed in definite points in the sky with relation to each other, the relative position of stars has remained about the same for many centuries. In certain groups of stars, primitive stargazers saw the shapes of creatures or heroes of their folklore. Names were applied to the shapes of these various groups of stars. Later, people saw in the stars the shapes of household implements with which they worked. The development of the names of stars began early in the history of man and finally resulted in a catalog of the visible stars. The named shapes became constellations, and the individual stars were identified by name with the constellation of which they were a part. From this primitive development, the constellations were given Latin names. Other groups of stars were assigned names of gods and goddesses and creatures of land and sea that figured in Roman and Greek mythology. Much later in history, our forefathers saw in the many constellations objects common to their mode of living. Thus, the Big Bear came to be known as the Big Dipper. To the English, this same constellation is the Plough. Some of the more familiar stars and constellations are described below.
a. The familiar constellation called the Big Dipper is only part of the constellation Ursa Major. (See Figure 7-28.) The seven stars of the dipper are easy to find on almost any clear night. The two outer stars of the bowl point toward the North Star, Polaris, which is about 30° away. The distance between the pointers is about 5°. Both measurements are very helpful when the star finder and identifier is being used.
b. Cassiopeia (Figure 7-29), sometimes called the Lady in the Chair, the Running M, or the Lazy W, is a prominent northern constellation. It is found directly across the celestial North Pole, opposite the Big Dipper. When the Big Dipper is below the horizon, Polaris can be found by drawing a line from the star Ruchbah bisecting the angle formed by the shallow side in Cassiopeia. The bisecting line points almost through Polaris.
c. Polaris, the polestar, is the alpha star in the constellation Ursa Minor (Figure 7-30), commonly called the Little Dipper. On a clear night, the Little Dipper is easily seen. The handle of the dipper has a reverse curve, and Polaris is the last star in the handle.
d. The first prominent constellation after the vernal equinox has risen in the east is Taurus, the Bull. (See Figure 7-31.) On the forehead of Taurus is a red star of the first magnitude, Aldebaran. It is a royal star, one of the four stars most commonly used by navigators. On the upper foreleg of Taurus is the Pleiades. This aggregation is a tight cluster of stars, which is also called the Seven Sisters.
e. Chasing these seven stars and the bull is Orion, the Hunter. (See Figure 7-32.) There are two very bright stars in Orion. The hunter's right shoulder is Betelgeuse ( Orionis); his left knee is Rigel ( Orionis). Close on the heels of Orion are his two dogs, Canis Major and Canis Minor. In the big dog is the brightest star in the sky, Sirius. It is a brilliant blue-white star. Slightly behind Canis Major is the smaller dog in which Procyon is found.
f. At about the same right ascension with the canine constellation is Gemini, the Twins. (See Figure 7-33.) Think of Gemini as a wedge pointed straight toward Orion. The bright star at the base of the wedge is Pollux ( Geminorum); the one above it is Castor ( Geminorum).
g. About 2 hours behind Gemini and Canis Minor is Leo, the Lion. (See Figure 7-34.) The head and forequarters of Leo are sometimes known as the Sickle. The body and tail extend off to the east. The heart of Leo is Regulus ( Leonis). Regulus is another of the four royal stars. It is brilliant white, whereas the others are red.
h. As soon as Leo is well up in the sky, Virgo (Figure 7-35) will rise in the east. The bright star in Virgo, called Spica ( Virginis). makes an approximately equilateral triangle with Denebola ( Leonis) and Arcturus ( Bootis). This triangle is sometimes called the Virgo triangle.
i. One of the most easily recognized constellations is Scorpio. (See Figure 7-36.) However, it is so far south that in northern latitudes it is visible during evening hours only through July and August. Antares ( Scorpii) is another of the four royal stars.
j. The Northern Cross, Cygnus, is found very close to the circumpolar region. (See Figure 7-37.) This is a very prominent constellation, and in northern latitudes in the fall, it will be nearly overhead in the evening. The head of the cross is Deneb ( Cygni). There are two neighbor stars in this sector of the sky--Vega ( Lyrae), which rises just before the cross, and Altair ( Acquilae), which trails it somewhat to the south. Cygnus is imagined by some to be a cross; to others, it takes the shape of a swan from which the name is derived.
k. Pegasus (Figure 7-38), which includes the Great Square, straddles the hour circle of the vernal equinox. This is the constellation of the flying horse, a very prominent skymark.
l. Fomalhaut, the fourth royal star, is a prominent star in the southern sky. It ranks number 13 in brightness of stars visible in the Northern Hemisphere.
Approximate azimuth and altitude to a selected survey star at a date and time chosen by the user can be determined by using DA Form 7284-R (Figures 7-39 and 7-40) and Program 7 of the SURVEY REV1 module. This orientation data will help identify survey stars for astro observation or navigation.
a. Capabilities. This program will compute the approximate azimuth and altitude (vertical angle) to any of the 73 survey stars selected by the user. These orientation data are accurate to ±5.0 mils for the date, time, and location selected for observation. The user can determine orientation data for any number of survey stars with the program, but he is limited to six sets of data per form. This program will enhance the surveyor's ability to identify stars in the Northern and Southern Hemispheres. It provides a tool for leaders to train surveyors to respond rapidly to astro observation requirements.
The altitude method can be used to determine azimuth from the sun or from the stars. This method requires the solution of the astronomic (PZS) triangle (Figure 7-20) by using, as determined data, the three sides of the triangle (polar distance, colatitude, and coaltitude). In the altitude method, the time is required only to determine the declination of the body. When the sun is observed, the time should be accurate within 5 minutes. For stars, only the date is required. Since time is not critical in the altitude method of observation, this method is used most frequently by artillery surveyors.
Stars for altitude observation should be in the east or west between 175 and 800 mils in altitude. When the sun or a star is observed, it should be within 530 mils of the observer's prime vertical. This is the arc on the celestial sphere that passes through points due east and west of the observer and through his zenith. The sun must not be within 2 hours of the observer's meridian. For the best results, the sun should be above 175 mils in altitude. Unless an elbow telescope or the card method (paragraph 7-14) is used, the sun must be below 800 mils in altitude.
a Parallax. The word parallax is defined as "the difference in altitude of a celestial body as seen from the center of the earth and from a point on the surface of the earth." An observed altitude of the sun is corrected for parallax; that is, for the error introduced by the fact that the observer is on the surface of the earth and not at the center. (See Figure 7-41.) This difference is negligible on vertical angles to the stars because they are so far from earth. The constant for the parallax of the sun is considered as +7 seconds, or +0.04 mil.
b. Refraction. Refraction (Figure 7-42) is the apparent displacement of the celestial body caused by the bending of light rays passing through layers of air of varying density. The refraction varies according to the altitude of the light source above the horizon. At a temperature of +70°, refraction of a body on the horizon is 10.26 mils; refraction of a body at the observer's zenith is 0 mils. Refraction increases with an increase in barometric pressure and a decrease in temperature. It decreases with a decrease in barometric pressure and an increase in temperature. The refraction correction is extracted from FM 6-300 (Table 1b) and is applied to observed altitudes of the sun and stars. The sign of the refraction correction is always minus.
a. In solving for azimuth as in other survey problems, a standard DA form has been designed to facilitate the necessary computations. DA Form 5594-R (Computation of Astronomic Azimuth by Altitude Method, Sun (BUCS)) (Figure 7-43) and DA Form 5595-R (Computation of Astronomic Azimuth by Altitude Method, Star (BUCS)) (Figure 7-44) have been designed to solve for azimuth by the altitude method formula. (Reproducible copies of both of these forms are included in the Blank Forms section of this book.)
b. The top portion of the DA forms is set up basically the same as the other BUCS forms you have used. The top six blocks are for administrative information. Below the administrative data, you will find notes that refer to the operation of the BUCS in this program. Under the notes on the left side of the form, you will find specific instructions on the use of this form. To the right of the instructions, you will find the data record where all known, field, and computed data are recorded. Blocks that are marked with a bold arrow are where field data are entered. One complete observation (three sets) can be recorded and computed on each form.
The fieldwork necessary for determining azimuth by the altitude method includes measuring the horizontal and vertical angles and recording the time of the observation and the temperature. The temperature should be recorded at the beginning of the observation and again when the observation has been completed. The mean temperature is used in the computation. The watch used in the observation should be checked with radio time signals to determine the watch correction. The time signals for the Western Hemisphere are broadcast by radio station WWV at Fort Collins, Colorado, at frequencies 2.5, 5, 10, 15, 20, and 25 megahertz (MHz). Signals for the Eastern Hemisphere, broadcast by station JJY at Koganei, Japan, can be received at frequencies of 2.5, 5, 10, or 15 MHz. Each minute during the day, a tone is sounded and the exact time of the tone is announced. The voice announcement begins about 10 seconds before the time signal with the words "At the tone, the time will be (time), universal coordinated time." This announcement is followed by the sounding of the tone. The time announced is universal time. Set the minute hand of the watch to be used exactly to the time signal. Make no attempt to set the second hand. Determine the watch correction by noting the position of the second hand at the time of the tone. Then record as the watch correction the number of seconds at which the second hand was positioned before or after the 0 second mark, along with the proper sign. The procedure for time signals elsewhere may vary slightly from those given above.
Particular attention should be paid to secure the best available data. Roughly, an error of 1 minute in latitude, declination, or altitude may cause a corresponding error of more than 0.5 mil in azimuth. Time is less important in a sun observation because an error of 5 minutes cannot change the azimuth more than 0.03 mil. For star observation, only the date is required.
a. Technique for Determining Azimuth for Fifth-Order Survey. To determine azimuth for a fifth-order survey by using the T16 theodolite, observe and compute at least three sets of observations (each set, one position). Mean the azimuths, and reject any set that varies from the mean by more than 0.3 mil. At least two sets must be meaned to determine final azimuth.
b. Technique for Determining Azimuth for Fourth-Order Survey. To determine azimuth for a fourth-order survey by using the T2 theodolite, observe and compute at least three sets of observations (each set, one position). Mean the three azimuths, and reject any set that varies from the mean by more than 0.150 mil. At least two sets must be meaned to determine the final azimuth.
ARTY ASTRO OBSERVATION METHOD (SUN)
In the arty astro method of determining azimuth, two sides of the PZS triangle (Figure 7-21), the polar distance and colatitude, and one angle are used to solve for the azimuth angle. This computation is based on the time of the observation. The problem of determining azimuth consists of taking a horizontal reading at the observer's station between the mark and sun, the azimuth of which can be computed. The simple operation of subtracting this horizontal angle from the computed azimuth of the sun gives the desired azimuth to the mark.
For observations by the arty astro method, the sun must not be within 1 hour of the observer's meridian. For best results, the sun should be above 175 mils in altitude. Unless an elbow telescope or the card method is used, the sun must be below 800 mils in altitude.
a. Arty astro is computed on DA Form 7285-R (Computation of Arty Astro (Sun/Star) (BUCS) (Figure 7-45). This form is basically the same as other forms used for computations with the BUCS. The administrative data are recorded on the bottom instead of on the top of the page. The left side of the form shows the instructions for use of the form, and the right side shows the data record where all field work, known data, and computed data are recorded. One complete observation can be recorded and computed on this form.
b. The instructions for computing DA Form 7285-R are shown in Table 7-4. Program 13 uses the "electronic ephemeris," which allows the observation to be computed by using the internal time module of the BUCS to determine the date and time for each observation. However, the date and time can be entered manually. If the internal clock is used, each set has to be computed before the next reading can be made.
ARTY ASTRO METHOD (STAR)
The arty astro method can be used with observations on Polaris or on east-west stars. Used with Polaris, this method yields the most accurate azimuths. When the arty astro method is used with east-west stars, the requirement for accurate time is a disadvantage, but the method can be used when no stars meet the position requirements for the altitude method. Computation of arty astro star is the same as the computations for arty astro sun. The only differences are steps 9 and 9a of the form. Step 9 will be answered N (no). Step 9a asks for the star number which can be found on the reverse of the computation form.
The star chart is used for selecting east-west stars for arty astro observations. Polaris should be observed anytime it is visible. Best results are obtained when it is above 175 mils in altitude to minimize the effects of refraction.
a. Polaris appears to move in a small, elliptical, counterclockwise orbit about the celestial North Pole. Because Polaris stays so close to the celestial North Pole, it is visible throughout the night in most of the Northern Hemisphere. When the Polaris local hour angle is 0 or 12 hours, the star is said to be in its upper or lower culmination, respectively. (See Figure 7-47.) When the Polaris local hour angle is 6 or 18 hours, the star is said to be in its western or eastern elongation, respectively. The small orbit of Polaris results in a very slow apparent motion, so the star can be observed at any point in its orbit. The least chance of error in tracking, however, will occur when the star is in elongation.
b. To help identify Polaris, set the latitude of the observer's position as a vertical angle on the observing instrument and point the telescope north. The line of sight will be near the celestial North Pole, and since Polaris is very near the pole, the star should appear in the field of view. If the star is in elongation, its altitude will equal the observer's latitude. When Polaris is moving from eastern to western elongation, its altitude is greater than the latitude of the observer. When Polaris is moving from western to eastern elongation, its altitude is less than the latitude of the observer.
c. When the telescope is directed at Polaris, the observer will see two other stars nearby that are not visible to the naked eye. However, Polaris will be the only star visible when the cross hairs are lighted.
POLARIS TABULAR METHOD
The computational methods discussed in Sections V, VI, and VII are satisfactory for both fourth-order and fifth-order work. The Polaris tabular method of computation will achieve reliable fourth- and fifth-order accuracies. The Polaris tabular method uses the azimuths to Polaris that are tabulated in FM 6-300, Table 12. These azimuths are corrected by factors related to the observer's latitude and the date and time of observation.
DA Form 5598-R (Computation of Astronomic Azimuth by Polaris Tabular Method (BUCS)) (Figure 7-48) is used to compute astronomic azimuth by the Polaris tabular method with a BUCS. (A reproducible copy of this form is included in the Blank Forms section of this book.)
a. The top portion of DA Form 5598-R is set up basically the same as the other BUCS forms you have used. The top six blocks are for administrative information. Below the administrative data you will find notes that refer to the operation of the BUCS in this program. Under the notes on the left side of the form, you will find specific instructions on the use of this form. To the right of the instructions, you will find the data record where all known, field, and computed data are recorded. Blocks that are marked with a bold arrow are where field data are entered. One complete observation can be recorded and computed on each form (three sets).
Simultaneous observations of a celestial body provide a quick method of transmitting direction over great distances without time-consuming computations. This method is ideally suited to the needs of the artillery since many units can be placed on common directional control in a very short period of time. Because of the great distance of celestial bodies from the earth, the azimuths to a celestial body at any instant from two or more close points on the earth are approximately parallel. The difference in the azimuth is caused by the fact that the azimuths at different points are measured with respect to different horizontal planes.
a. Flank stations are established at points where azimuth is required. A master station is established at a point from which the grid azimuth to an azimuth mark is known or has been computed. (See Figure 7-49.) (An assumed azimuth may be used.) Both the flank and master stations should be points that are easily identified on a map and provide the best possible communications.
b. An observing instrument is set up at the master station and oriented on the azimuth mark. An observing instrument is set up at each flank station and oriented on a reference mark to which the azimuth is required. (See Figure 7-50.) The observing instrument at the master station must be of equal order as, or higher order than the instrument used at the flank station. A prominent celestial body is selected by the observer at the master station and identified to the observer at each flank station. On command, an assistant will key the microphone so the observer can transmit information at the same time he observes a celestial body. A headset, loudspeaker, or other device must be provided for the observer at each flank station so he can hear instructions from the observer at the master station. When all stations are ready to observe, the master station observer announces READY, START TRACKING (countdown), TIP. Each flank station observer, when observing a star, places the vertical cross hair of his instrument on the star and keeps it there by using the horizontal recording motion tangent screw. When observing the sun, he centers the sun inside the solar circle. He keeps it centered by using the tangent screws. The master station observer announces TIP at the instant the star is at the intersection of the cross hairs or when the sun is centered in the solar circle. The observer at the master station records the readings on the horizontal and vertical scales. Each flank station observer records the reading on the horizontal scales. All observers then plunge their telescopes and repeat the tracking procedure.
c. At the master station, the measured horizontal angle is added to the known azimuth to the mark to determine the azimuth to the sun. The grid coordinates of the master station, the vertical angle to the sun, and the grid azimuth of the sun are transmitted to each flank station. The flank station operator plots on his map a line representing the azimuth from the master station to the celestial body. From the flank station, a line is drawn perpendicular to the line representing the azimuth from the master station to the celestial body. (See Figure 7-50.) The flank station observer then determines the correction to be applied to the azimuth from the master station to the celestial body. When this correction is applied (added or subtracted), the result is the azimuth from the flank station to the celestial body. The correction is determined by using the correction nomograph in Figure 7-51 (or Table 13 of FM 6-300).
d. The nomograph consists of three columns. The left column is graduated in meters from 100 to 1,000. It represents the value of the length of the line (D) from the flank station to the plotted line that represents the azimuth to the sun from the master station. The center column is graduated in seconds and mils from 0.5" to 70" and from 0.003 mil to 0.34 mil and is the correction (C). The right column is graduated in degrees and mils from 10° to 65° and from 180 mils to 1,150 mils. It represents the vertical angle to the celestial body at the master station (H). Before C can be determined, the values of D and H must be known and used as arguments in the nomograph. When the distance exceeds 1,000 meters, it must be divided by 10, 100, or 1,000 to obtain a value between 100 and 1,000. In such cases, the chart value of C must be multiplied by the same value by which the distance was divided. The value H must be between 180 and 1,150 mils. If the flank station is to the left of the line from the master station to the celestial body, the sign of the correction is plus; if the flank station is to the right the sign of the correction is minus.
e. When the azimuth to the sun from the flank station has been determined, the measured horizontal angle is subtracted. The result is the azimuth to the azimuth mark at the flank station.
a. Simultaneous observations are comparable in accuracy to an astro observation with a theodolite or aiming circle. The accuracy cannot exceed that of the instrument used. Requirements for the various accuracies are discussed below.
- A known azimuth of fourth-order or better and a T2 theodolite at the master station.
- A T2 theodolite at the flank station.
- An azimuth of fifth-order or better and a T16 or T2 theodolite at the master station.
- T16 at the flank station.
- An azimuth of fifth-order or better and a T16 theodolite at the master station.
- An aiming circle at the flank station.
(1) Requirements for fourth-order azimuth (± 0.150 mil) are as follows:
(2) Requirements for fifth-order azimuth (+0.3 mil) are as follows:
(3) Requirements for 1:500 azimuth (±0.5 mil) are as follows:
(4) Specifications are the same as for an astro observation (Appendix B).
b. When a T16 theodolite is used at a flank station and a T2 theodolite is used at the master station and the conditions of a above are met, the maximum accuracy that can be realized will be fifth-order azimuth or ±0.3 mil. If the master station instrument is a T16 theodolite and the flank station instrument is an aiming circle, the maximum accuracy to be expected is ±0.5 mil.
Note. Simultaneous observations will yield the same accuracy as astro azimuths taken with the instructions used to a maximum D value of approximately 26,000 meters. Observations may be conducted over much longer distances if a 1-mill or 2-mil accuracy is acceptable.
a. This method enables battalion surveyors and firing battery personnel to compute a grid azimuth and a check angle from observations of the sun or a selected survey star. The accuracy of the computation depends on which instrument is used to perform the observations (M2A2 aiming circle ±2.0 mils or T16 theodolite ±0.3 mils).
b. The fieldwork for this method is the same as the fieldwork for a flank station simultaneous observation. The hasty astro program is the master station for the observation. A T2 does not have a nonrecording motion; therefore, it will not be used in conjunction with this method.
(2) Place 0000.0 mils on the horizontal scale. Lock the scale with the horizontal clamp.
(3) Track the celestial body (with scale locked), and announce TRACKING when the instrument is oriented on the sun or selected survey star. Announce TIP when the center of the reticle is exactly aligned on the sun or star.
(5) When the grid azimuth to the celestial body at the time of tip is displayed, record this as the azimuth to the EOL.
(6) Depress the telescope, and emplace the EOL.
(7) Unlock the scales, and repeat steps 3 and 4. The BUCS will display the check angle. Compare the check angle from the BUCS to the check angle on the instrument. If the difference is ±2.0 mils for the aiming circle and ±0.3 mil for the T16 theodolite, the azimuth to the EOL is good; if not, check all data and/or reobserve.
d. Azimuth from the hasty astro method is computed with BUCS by using DA Form 7286-R (Computation of Hasty Astro (BUS)) (Figures 7-53 and 7-54) and Program 6. (A reproducible copy of this form is included in the Blank Forms section of this book.) This program uses the electronic ephemeris, which eliminates the need to extract ephemeris data from FM 6-300. This program provides the option of using the internal timer to determine the date and time of tip for each observation or to input the date and the time manually. The ability to manually input the date and time of observation allows surveyors to perform fieldwork without the BUCS at the site of observation.
SELECTION OF METHODS OF OBSERVATION
The method selected for observation depends upon the observer's location, celestial bodies available, and the accuracy required. During daylight hours, only the sun is available. The observer's location will dictate if the altitude method or the arty astro method must be used. At night, the determining factors will be the availability and locations of the stars.
a. Generally, speed of computation is the most important consideration in choosing a method for fifth-order astro azimuth determination. The techniques covered in Sections V, VI, VII, and VIII are all satisfactory for fifth-order azimuth determination.
b. At night, in the Northern Hemisphere, Polaris should always be used if it is observable, because it is easy to identify and easy to track. When observing Polaris, use either the arty astro method or the Polaris tabular method. If Polaris is not visible but an east-west star is, either the altitude method or the arty astro method can be used. If the star has a high star rate and accurate time is available, use the arty astro method. If the star has a low rate, the altitude method generally is preferable because it requires less accurate time than does the arty astro method. If time is not critical and only east-west stars are observable, observe a star in the east and one in the west.
c. In the daytime, use the sun-altitude method if the sun is in the proper position, since accurate time is not so important as it is with the arty astro method. If the sun is not in the proper position to use the altitude method, use the arty astro method.
a. Generally, the prime consideration in choosing a method of fourth-order azimuth determination is accuracy. Theoretically, the arty astro method is more accurate than the altitude method, but this accuracy depends in turn on the availability of accurate time.
b. The best source of fourth-order accuracy is the Polaris arty astro method. (Polaris is never observed by the altitude method.) Polaris is easily identified and tracked, and when the arty astro method is used with Polaris, accurate time is not so critical as it is when used with an east-west body. The Polaris tabular method will yield reliable fourth-order azimuths. When Polaris cannot be seen, observe an east-west star with the arty astro method if accurate time is available. If time is unreliable, use the altitude method of observation.
c. In the daytime, use the arty astro method with the sun if accurate time is available; if not, use the altitude method.
During daylight hours, the sun is the only celestial body that can be readily observed. At night, Polaris is one of the most easily identified stars in the Northern Hemisphere. It is ideal for observation because of its slow movement. However, Polaris cannot be seen in many parts of the Northern Hemisphere because of local weather conditions, and it cannot be used in areas close to the equator and in the Southern Hemisphere. Therefore, it is inadvisable to depend solely on this star for night observations. Methods of identification and approximate locations of the stars on the celestial sphere in relation to the observer's position are presented in Section IV. All artillery surveyors must be familiar with the more common stars and their relative positions in the sky.
The primary considerations in selecting a method of determining azimuth are as follows:
- The time available to the observer.
- The instruments available for the observer's use.
- The observer's knowledge of the correct time.
- The observer's experience in astro observations.
The secondary consideration is the degree of accuracy desired. Refer to Table 7-7 for a comparison of azimuth determination methods.
The Army must be prepared to undertake field operations at any location on the earth. Hence, the artillery surveyor must be able to function effectively at any and all locations, to include those in the Southern Hemisphere.
a. Locations within the Southern Hemisphere present new problems to an observer accustomed to working the PZS triangle in the Northern Hemisphere. The coaltitude, colatitude, and local hour angle are computed in the same manner as in the Northern Hemisphere. However, other techniques must be used in determining the polar distance and true azimuth.
b. The polar distance is determined by algebraically adding the declination of the celestial body to 90° (1,600 mils) with due regard for the algebraic sign of the declination. In the Southern Hemisphere, the true azimuth to the celestial body is determined by adding the azimuth angle to or subtracting it from 3,200 mils. If the celestial body is west of the observer, the azimuth angle is added to 3,200 mils; if the body is east of the observer, the azimuth angle is subtracted from 3,200 mils. (See Figure 7-55.)
Note. In Figure 7-55. Angle 1 at celestial North Pole is the same as Angle 3 at the celestial South Pole. Angle 2 at the celestial North Pole is the same as Angle 4 of the celestial South Pole.
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